Demodulator — Control Systems/Waveform Functions

Demodulator

Control Systems / Waveform Functions

Recovers the message from an amplitude-modulated carrier by coherent detection: multiply by a local carrier of the same frequency, then low-pass what is left.

m[k] = g·y[k]·f(θ[k]) and x[k] = lowpass(m)[k] − d, with θ[k] = 2πF_c·k·T_s, g the mixer gain, f the carrier function and d the Output Offset. The lowpass is a Butterworth of the configured order and cutoff.

The Detection setting picks g and f, and those two choices are the whole difference between an AM detector and either arm of a QAM one.

Ports

• y – the modulated signal, scalar. Nothing is assumed about its amplitude.
• x – the recovered message, scalar, in the message's own units.

Parameters

• Detection – which detector the block is.
  • AM – g = 1 and a cosine carrier, the default. This is the branch MATLAB's demod takes for 'am', 'amdsb-sc', 'amdsb-tc' and 'amssb' alike: all four share one mixer and one filter, and the only thing that distinguishes 'amdsb-tc' is the offset below.
  • QAM in-phase – g = 2 and a cosine carrier, the first output of demod(…, 'qam').
  • QAM quadrature – g = 2 and a sine carrier, its second output. Wire one of each to recover both messages.
• Carrier Frequency (Hz) – F_c, which must be the frequency the signal was modulated at; detection is coherent, so a carrier even slightly off beats against the message rather than removing it. Its magnitude also supplies the default cutoff below.
• Lowpass Order – the Butterworth order, a whole number from 1 to 10. 5 is the default because it is the order MATLAB's function uses. Above 10 the block refuses rather than designing, since every export target unrolls the recursion into one straight-line block.
• Lowpass Cutoff (Hz) – where the filter turns over. Zero or less means "use the carrier frequency", which is demod's own choice (butter(5, Fc*2/Fs) is a cutoff at F_c). A cutoff is clamped inside (0, half the sampling rate), which is the only interval a digital filter can be designed in.
• Output Offset – d, subtracted from the filtered result. This is demod's fifth argument for 'amdsb-tc': the constant the modulator added so its carrier would never vanish. Leave it at zero for every other method.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text.

The filter is designed once, here, and its coefficients are inlined. The order and the cutoff are configuration and the rate is the block's own, so no exported core computes a tangent, a pole or a bilinear map – each one receives the finished numerator and denominator as literals and runs the recursion. Everything is therefore structural, the period included: a core exported at one rate carries a filter designed for that rate, so re-export after changing the rate, the order, the cutoff or the frequency.

The three HDL targets are simulation-only and carry the block in real arithmetic, quantizing only at the port boundary. A Butterworth whose cutoff is well below the sampling rate has poles close to the unit circle – at order 5 with a cutoff of 3.4 Hz at 100 Hz the recursion's leading coefficient is −4.31 – and a Q16.16 datapath subtracting large nearly-equal terms has nothing left of the signal. A synthesizable version is a different filter structure, not a different export.

Simulink bridge

No equivalent (Support::None). demod is a Signal Processing Toolbox function, and that toolbox ships no Simulink library at all. The demodulator blocks in the installed libraries belong to Communications Toolbox and are different blocks, carrying symbol decisions and a complex baseband convention this block does not, so mapping onto one would misreport what crossed. The bridge reports this block instead, and it carries no parity testbench; code export verification covers it across all ten languages.

Notes

• Stateful – the carrier phase and the filter's N delay elements – and discrete by nature (setDiscreteOnlyBlock(true)).
• The filter runs once, forwards. MATLAB's runs filtfilt. That is a different estimator, not an approximation of the same one, and it is offered here as itself: a zero-phase filter runs forwards and then backwards over the whole record, which a block that sees one sample at a time cannot do at any price. The consequences are a phase lag where filtfilt has none, and a startup transient where filtfilt has none. Measured against R2026a on a 0.7 Hz message at F_c = 3.4 Hz and F_s = 100 Hz, order 5, cutoff at the carrier: the two differ by at most 0.248 where the message's rms is 0.462 – and that difference is the lag, not a distortion. Shifting this block's output back by the 15 samples of group delay the filter has at that message frequency leaves at most 0.043. It is not a startup effect either: the worst sample of the 500 is number 357. If the zero-phase result is what you need, filter offline; this block is the one that runs in a generated core. The tree's Signal Smoothing / Zero-Phase Filter block is the other answer.
• The design agrees with butter. Same prototype, same prewarped bilinear map as Polynomials / Butterworth Design, checked against R2026a: butter(5, 0.068) to 1.8×10⁻¹⁵ and butter(3, 0.24) to 4.4×10⁻¹⁶. Reach for that block instead when the cutoff has to arrive on a port; this one designs from configuration only.
• Detection is coherent and the phase is not recovered. The local carrier starts at θ = 0 and runs at exactly F_c; nothing here locks it to the incoming signal. A modulator and a demodulator started together in one model agree by construction, and a signal arriving with an unknown phase needs a carrier recovery loop this block does not contain.
• The output lags, and by how much is worth knowing before you wire it to anything. A causal lowpass delays what it passes; measured at order 5 with the cutoff at a 3.4 Hz carrier and a 100 Hz rate, a 0.7 Hz message comes out 15 samples late, and the delay grows both with the order and as the message approaches the cutoff. A lower order or a wider cutoff buys latency at the cost of leaving more of the carrier's second harmonic in the result.
• Scalar only: one signal, one carrier phase, one filter state. Wire one block per channel.
• No state space. The mixer multiplies the input by a time-varying quantity, so the block is not time-invariant and model reduction correctly declines to merge it – even though the filter behind the mixer is linear.